Robust run order for uniform designs in simple linear regression with MA errors

Abstract

This work investigates the best run order for a simple linear regression model under a uniform design when errors follow a MA(1) or a subset MA(k) process where k is a positive integer. Based on a robust criterion for experimental designs proposed by Zhou [6],it is of interest to find a way to arrange the run order of a given uniform design on [-1,1] to minimize the robust criterion for estimating the slope. The optimal run order will be presented where the order structure is decomposed into three categories to obtain the optimal solution. A numerical study is conducted to investigate the behavior of the coverage probability for estimation of the slope parameter.